Three is a crowd

Number Theory Level 3

Find all the three digit numbers abc‾\overline{abc} such that abc‾=(a+b+c)2+a+b+c.\overline{abc}=(a+b+c)^2+a+b+c. Enter your answer as the sum of all such three digit numbers.

Stratos Giakoumakis by Stratos Giakoumakis
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